Geometric biopsy plan optimization

ABSTRACT

The present invention is directed to a method for calculating tumor detection probability of a biopsy plan and for generating a 3D biopsy plan that maximizes tumor detection probability. A capsule shaped volume is modeled to represent the volume that a biopsy core may sample. An optimization method is used to generate a 3D biopsy plan that maximizes probability of tumor detection for predefined biopsy core numbers and length. Risk of detecting insignificant tumors, also determined by size, and probability of a false negative result is automatically calculated. The present invention also includes a method to determine number and length of biopsy cores required for individual patients determined by the balance of the insignificant/significant probability of detection, prostate size and shape, based upon the previously explained 3D biopsy plan generation method.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional PatentApplication No. 62/409,040, filed on Oct. 17, 2016, which isincorporated by reference herein, in its entirety.

FIELD OF THE INVENTION

The present invention relates generally to biopsy. More particularly thepresent invention relates to a method for geometric biopsy planoptimization.

BACKGROUND OF THE INVENTION

In 2014, an estimated 233,000 new cases of prostate cancer (PCa) werediagnosed in the US alone. Studies have shown that it is necessary totreat many men to prevent one death from PCa and that significantovertreatment exists. Even so, PCa caused an estimated 29,480mortalities in 2014 alone. This data underscores the need for morespecific PCa screening tests and more reliable PCa diagnosis at biopsy.

Systematic, untargeted prostate biopsy is the current gold standard forPCa diagnosis. Ideally, the goal is to uniformly distribute the biopsycores according to an extended sextant biopsy plan. But a coordinatebased geometric definition of the biopsy plan is typically unavailable.Rather, current biopsy plans are simplistically represented by a twodimensional (2D) cross-section of the gland showing a grid of points.This leaves room for subjective interpretation. Moreover, the number andlength of the biopsy cores are not typically optimized for individualpatients.

The most common way of diagnosing PCa is the transrectal ultrasound(TRUS) guided prostate biopsy. More than 1 million procedures areperformed each year in the United States and Europe. While targetedbiopsy methods (currently using ultrasound to magnetic resonance imaging(MRI) fusion) are being investigated for high risk patients, the mostnumerous, primary biopsies are still performed based on TRUS guidedsystematic extended sextant biopsy plans that are supposed to sample thegland uniformly. However, clinical data shows that systematic biopsieshave low sensitivity and low negative predictive value. Studies haveconfirmed that biopsy samples are often clustered and miss regions,leading to both over- and under-sampled regions of the prostate, whichincrease the likelihood of detecting insignificant cancer and obtainingfalse negative biopsy results. Among other factors such as manualexecution errors, biopsy planning is a major cause of unreliableprostate biopsy localization.

The current systematic extended sextant plans are poorly defined from ageometric standpoint. The typical 12-core extended sextant biopsy is touniformly sample at Left/Right×Medial/Lateral×Apex/Mid/Base of theprostate. The current representation of the plan is a schematic of agrid of points on a 2D coronal section of the prostate. The basic andextended sextant plans, for example, are shown in FIG. 1A and FIG. 1B.This definition is vague, lacking the coordinate location of the coresand leaving much room for subjective interpretation. In 3D theuncertainty widens, as exemplified in FIG. 1C. It is unclear where theplane of grid should be, or whether the cores should be coplanar.

An optimal biopsy plan should be defined by 1) the number of cores and2) core coordinate locations and directions. Several studies have beenconducted to compare different number of cores (e.g. 6, 8, 12, 14, 20cores), locations (e.g. additional cores in the apex), and directions(e.g. more lateral). Meanwhile, the American Urological Association(AUA) has recommended to use the 12-core extended sextant plan withapical and far-lateral locations of the gland, based on a literaturereview of clinical results.

However, other authors have reported mixed results, for exampledifferent detection rates for the same number of cores and higherdetection rate with fewer cores. Possible reasons of this inconsistencymay be due to patient selection differences in core placement betweenurologists for the same biopsy plan, and low repeatability of biopsyeven for the same urologist. Moreover, false-negative biopsy rates couldnot be evaluated in these studies since the reference tests were basedon radical prostatectomy specimens, suggesting that the true PCadetection rate could be even lower.

Biopsy plans are not typically customized for individual patients. Theonly parameter that may sometimes change the biopsy plans is theprostate volume. Yet it remains unclear if and how the biopsy planshould be adjusted for different prostate volume and the 12-core planremains commonly used regardless of the volume. It was, however,suggested that since there is large variation in prostate volumes (from10 cm³ to hundreds of cm³) biopsy core numbers need to be adjustedaccordingly. Yet, other clinical studies found that there is noadvantage on increasing the number of cores for larger prostates,leaving the debate still open.

Computer simulated biopsy studies have been performed based onstatistical atlases using whole mount prostates. In these studies, thedetection rates of different biopsy plans were measured by calculatingthe number of tumors detected by the simulated biopsy cores, and thenumber of tumors missed in each case. These groups have been first topropose and implement analytical prostate biopsy optimizations byprecisely calculating the number of cores needed to achieve a certaindetection rate. Among them, results were somewhat different possibly dueto different statistical maps of tumor occurrence used by each group, ordifferent placement of the cores for the same biopsy plan. Because themethods were used on the resected gland, they could not consider thepath of needle insertion.

Other previous approaches used 2D analyses to determine the probabilityof significant cancer detection for transperineal biopsy using a gridtemplate of equally spaced holes. This probability is calculated basedon the area covered by the cores per unit grid on the transversal 2Dcross section. The study demonstrated the ability to precisely calculatethe probability based on prostate geometry and was able to predict theprobability of a false negative result for an individual patient.

It would therefore be advantageous to provide a method that improvestumor detection probability of a given biopsy plan.

SUMMARY

According to a first aspect of the present invention a method ofcalculating tumor detection probability of a biopsy plan includingcalculating insignificant tumor detection probability. The methodincludes generating a three-dimensional biopsy plan that increases theprobability of the insignificant tumor detection probability.Additionally, the method includes calculating probability of a falsenegative detection of tumor using the three-dimensional biopsy plan, anddetermining a number and length of biopsy cores required to execute thethree-dimensional biopsy plan.

In accordance with an aspect of the present invention, the methodincludes implementing the method using a non-transitory computerreadable medium. The method also includes calculating tumor detectionprobability with steps such as, setting a bounding box for a tumordetection area and a voxel size to discretize this volume at apredetermined level of resolution; iterating through all voxels;checking if a voxel center is within the tumor detection area, and if soadd it to a set Γ; iterating through all voxels of set Γ; verifying ifthe voxel center falls within any of the biopsy cores of a set Π;counting the voxel with a center that falls within any of the biopsycores of set Π as sampled by adding it to a set Ω; and calculating tumorprediction probability as the ratio of the number of elements of the Ωand Γ sets. Additionally, the method includes detecting tumors in theprostate gland, and representing the biopsy cores as a capsule with acylindrical volume having hemispherical end caps. The method includessetting a tumor detection area. The method includes generating thethree-dimensional biopsy plan for significant tumors for a predefinednumber of biopsy cores and lengths. The method also includes generatingthe three-dimensional biopsy plan for insignificant tumors for apredefined number of biopsy cores and lengths. Additionally, the methodincludes defining a tumor detection area of a biopsy core as a capsulesurrounding the biopsy core with a cylindrical volume havinghemispherical end caps of the diameter of a tumor to be detected.

In accordance with still another aspect of the present invention, asystem for calculating tumor detection probability of a biopsy planincludes a source of image data capable of reconstructing a target organin three-dimensions. The system includes a non-transitory computerreadable medium. The non-transitory computer readable medium isprogrammed for calculating significant and insignificant tumor detectionprobability from the image data. The program also includes generating athree-dimensional biopsy plan that increases the probability of thesignificant and insignificant tumor detection probability andcalculating probability of a false negative detection of tumor using thethree-dimensional biopsy plan to create a revised three-dimensionalbiopsy plan. The program further includes determining a number andlength of biopsy cores required to execute the revised three-dimensionalbiopsy plan.

In accordance with yet another aspect of the present invention, thesystem further includes a computing device. The system includescalculating tumor detection probability with steps of setting a boundingbox for a tumor detection area and a voxel size to discretize thisvolume at a predetermined level of resolution; iterating through allvoxels; checking if a voxel center is within the tumor detection area,and if so add it to a set Γ; iterating through all voxels of set Γ;verifying if the voxel center falls within any of the biopsy cores of aset Π; counting the voxel with a center that falls within any of thebiopsy cores of set Π as sampled by adding it to a set Ω; andcalculating tumor prediction probability as the ratio of the number ofelements of the Ω and Γ sets. The system includes calculating tumordetection probability with steps of setting a volume of a tumordetection area and a voxel size to discretize the volume of the tumordetection area at a predetermined level of resolution to a set of voxelsΓ; defining the tumor detection area of a biopsy core as a capsulesurrounding the biopsy core with a cylindrical volume havinghemispherical end caps of the diameter of the tumor to be detected;iterating through all voxels of Γ and checking if a voxel center iswithin the tumor detection area of the biopsy cores of the plan; addingthe voxel center to the sampled voxel set Ω; and calculating tumorprediction probability as the ratio of the number of elements of thedetected voxel set Ω and tumor search area voxel set Γ. The systemincludes detecting tumors in the prostate gland. The system includesdetecting tumors in any organ with a boundary that is segmentable as asurface. The system includes representing the biopsy cores as a capsulewith a cylindrical volume having hemispherical end caps. Further thesystem includes setting a tumor detection area. The system can alsoinclude a biopsy device.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings provide visual representations which will beused to more fully describe the representative embodiments disclosedherein and can be used by those skilled in the art to better understandthem and their inherent advantages. In these drawings, like referencenumerals identify corresponding elements and:

FIGS. 1A-1C illustrate schematic views of biopsy schemes in 2D and anexample of its application in 3D.

FIG. 2 illustrates a schematic view of a model prostate with a tumor anda representation of a spherical model tumor being undetected by biopsycores.

FIG. 3A illustrates a schematic view of a definition of a capsule model.

FIG. 3B illustrates a schematic view of a modeled prostate with detectedand undetected tumors.

FIG. 4 illustrates a schematic view of detected and undetected tumorcalculation based on the capsule model.

FIG. 5A illustrates an image view of anatomical constraints for atransrectal biopsy.

FIG. 5B illustrates an image view of anatomical constraints for atransperineal biopsy.

FIG. 5C illustrates an image view of anatomical constraints for anangled biopsy.

FIG. 6A illustrates a schematic view of an initial biopsy plan for atransrectal biopsy.

FIG. 6B illustrates a schematic view of an initial biopsy plan for atransperineal biopsy.

FIG. 6C illustrates a schematic view of an initial biopsy plan for anangled biopsy.

FIG. 7A illustrates a transverse view reconstructed VHP model.

FIG. 7B illustrates a sagittal view of the reconstructed VHP model.

FIG. 8A illustrates a schematic view of a transrectal biopsy plan.

FIG. 8B illustrates a schematic view of a uniform grid biopsy plan.

FIG. 8C illustrates a schematic view of an angled needle transperinealbiopsy.

FIG. 9 illustrates schematic views of biopsy plans. FIG. 9 shows atransrectal 12-core, 18 mm core length biopsy of 40 cm³ prostate. Thesystematic plan is shown on the left and the optimized plan is shown onthe right with capsules (top) and cores (bottom). The optimizationincreases the probability of significant tumor detection (^(s)P) from42.5% to 54.4%.

FIG. 10 illustrates a graphical view of iterative improvement in theprobability of detection during the optimization process for anexemplary 20 cm³ prostate size.

FIG. 11A illustrates a graphical view of ^(s)P versus the number ofcores for different prostate sizes.

FIG. 11B illustrates a graphical view of ^(i)P versus the number ofcores for different prostate sizes.

FIG. 11C illustrates a graphical view of ^(s)P/^(i)P versus the numberof cores for different prostate sizes.

FIG. 12A illustrates a graphical view of a graphical view of ^(s)Pversus core length for different prostate sizes.

FIG. 12B illustrates a graphical view of ^(i)P versus core length fordifferent prostate sizes.

FIG. 12C illustrates a graphical view of ^(s)P/^(i)P versus core lengthfor different prostate sizes.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The presently disclosed subject matter now will be described more fullyhereinafter with reference to the accompanying Drawings, in which some,but not all embodiments of the inventions are shown. Like numbers referto like elements throughout. The presently disclosed subject matter maybe embodied in many different forms and should not be construed aslimited to the embodiments set forth herein; rather, these embodimentsare provided so that this disclosure will satisfy applicable legalrequirements. Indeed, many modifications and other embodiments of thepresently disclosed subject matter set forth herein will come to mind toone skilled in the art to which the presently disclosed subject matterpertains having the benefit of the teachings presented in the foregoingdescriptions and the associated Drawings. Therefore, it is to beunderstood that the presently disclosed subject matter is not to belimited to the specific embodiments disclosed and that modifications andother embodiments are intended to be included within the scope of theappended claims.

The present invention is directed to a method for calculating clinicallysignificant tumor (determined by size) detection probability of a givenbiopsy plan and a method for generating a 3D biopsy plan that maximizesthis tumor detection probability with a predefined number of biopsycores and core length. A capsule (cylindrical with hemispherical ends)shaped volume that is coaxial and centered on the biopsy core is modeledto represent the volume that a biopsy core may sample. A tumor isconsidered detected if its center is within this capsule, assuming thattumors are spherical. For a single core biopsy, sampled volume isdefined as the volume of the intersection between the respective capsuleand the prostate. The probability of detecting a significant tumor,determined by its size, with this single core is the ratio of sampledvolume to total prostate volume. For multiple core biopsy, theprobability of detecting a significant tumor is defined as the ratio ofthe combined, non-overlapping volume of individual sampled volumes tototal prostate volume.

An optimization method is used to generate a 3D biopsy plan thatmaximizes probability of tumor detection for predefined biopsy corenumbers and length. The risk of detecting insignificant tumors, alsodetermined by size, and the probability of a false negative result isalso automatically calculated. The present invention also includes amethod to determine the number and length of biopsy cores required forindividual patients determined by the balance of theinsignificant/significant probability of detection, prostate size andshape, based upon the previously explained 3D biopsy plan generationmethod.

The actual tissue volume extracted from a biopsy core is very small, onthe order of 0.005 cm³ for a typical 18 Ga prostate biopsy needle. Thisrepresents only 0.02% of a 24 cm³ prostate. It would then follow that4,800 needles would be required to fully sample the prostate.Fortunately, searching for clinically significant tumors requiressubstantially less cores.

To develop the tumor detection probability model, it is assumed thattumors are spherical in shape. Although many tumor foci are notspherical, this model is the worst-case scenario because the sphere hasthe lowest surface to volume ratio making it hardest to detect per unitvolume. In other words, the furthest distance between any two points issmallest on the sphere than any other shape of the same volume, asexemplified in FIG. 2. Therefore optimizations based on the sphericalmodel will result in the highest density of biopsy cores. The sphericalmodel also offers the advantage of simplicity which enables thedevelopment of the capsule model presented in the next section.

Next, it is assumed that the probability of tumor occurrence is uniformthroughout the prostate volume, although the majority of tumors occur inthe peripheral zone of the prostate. This also represents a worst-casescenario, since only sampling certain regions of the prostate wouldrequire less biopsy cores. In addition, the probability of tumoroccurrence in different zones of the prostate could be implemented byapplying weight factors to the regions based on statistical data.

Finally, the threshold of clinically significant tumor size is definedas ≥0.5 cm³ (sphere radius 4.924 mm) and insignificant tumor size≤0.2cm³ (radius 3.628 mm).

The optimization algorithm attempted to find as many as possible of thelarge tumors (≥0.5 cm³). Unavoidably, this process also resulted in thedetection of small tumors (≤0.2 cm³), which are undesirable to besampled. Tumors that fall in the midrange size (>0.2 cm³ & <0.5 cm³)were not searched for, but not considered detrimental if found.

A real tumor was considered sampled if the biopsy core intersected thetumor. In the model, a spherical tumor was sampled if the axis of core(needle) intersected the sphere. From the computational standpoint,however, it is more convenient to assess if the center of the sphere islocated within a capsule (a cylindrical shape with rounded ends) that iscentered on the core. These two approaches were equivalent in terms ofthe tumor being sampled or not, as shown in FIGS. 3A and 3B.

The capsule model is a cylindrical shape with hemispherical ends (FIG.3A). The radius of the capsule is equal to the radius (R) of thespherical tumor, and the length (L) of the cylinder equals the length ofthe core (biopsy core magazine slot on the needle).

This model allowed us to quantify the prostate volume that a needlesampled. Prostate biopsy needles are usually slim (18 Ga), making itconvenient to neglect their thickness. This also represents a worst casescenario since the modeled volume is less than the actual.

A spherical tumor is considered detected if, and only if, the distancefrom its center to the axis of the needle is smaller than its radius(d≤R), which makes the center fall within the capsule. Therefore, thevolume searched for a spherical tumor of radius R by a single needlecore is the volume of the capsule with the radius of the sphere and thelength of the core. FIG. 3B illustrates in 3D a spherical tumor beingdetected or not detected by the capsule model.

Numerically, the volume of the capsule is,

$\begin{matrix}{V_{C}^{R} = {{\pi\; R^{2}L} + {\frac{4}{3}\pi\; R^{3}}}} & \left( {{Eq}.\mspace{14mu} 1} \right)\end{matrix}$

The volume searched by one core within the prostate is,V _(s,1) ^(R) =V _(p) ∩V _(C) ^(R)  (Eq. 2)

For multiple cores, individual core volumes do not simply sum up becausethe cores may intersect each other. Therefore,V _(s,n) ^(R) =V _(p)∩(V _(c,1) ^(R) ∪V _(c,2) ^(R) . . . ∪V _(c,n)^(R))  (Eq. 3)

The probability of detecting a tumor of radius R with n cores is:

$\begin{matrix}{P_{n}^{R} = {\frac{V_{s,n}^{R}}{V_{p}} = \frac{V_{p}\bigcap\left( {V_{c,1}^{R}\bigcup{V_{c,2}^{R}\mspace{14mu}\ldots}\bigcup V_{c,n}^{R}} \right)}{V_{p}}}} & \left( {{Eq}.\mspace{14mu} 4} \right)\end{matrix}$

Since the radii of the significant (0.5 cm³) and insignificant (0.2 cm³)tumors are 4.924 mm respectively 3.628 mm, the significant andinsignificant probabilities of detection are:^(s) P=P ^(4.924) and ^(i) P=P ^(3.628)  (Eq. 5)

The P, either significant or insignificant, is a function of theposition and orientation of the biopsy cores relative to the gland. Coreorientation may be conveniently parameterized by the location of theentry point of the biopsy needle and the position of the core center.Therefore, a biopsy plan for n cores may be defined as a state matrixΠ(n×6) as:

$\begin{matrix}{\prod{= \begin{bmatrix}e_{11} & e_{12} & e_{13} & c_{11} & c_{12} & c_{13} \\\vdots & \vdots & \vdots & \vdots & \vdots & \vdots \\e_{n\; 1} & e_{n\; 2} & e_{n\; 3} & c_{n\; 1} & c_{n\; 1} & c_{n\; 3}\end{bmatrix}}} & \left( {{Eq}.\mspace{14mu} 6} \right)\end{matrix}$

Where, E_(ij)(e_(i1), e_(i2), e_(i3)) and C_(ij)(c_(i1), c_(i2), c_(i3))are the needle entry point respectively the core center positions ofcore i.

Then, the P can be calculated using the following algorithm:

-   -   Set a bounding box for the prostate and a voxel size to        discretize this volume at a desired level of resolution. For        simplicity, the coordinate system is the same of the image, but        could be differently chosen.    -   Iterating through all voxels, check if the voxel center is        within the prostate gland, and if so add it to a gland set Γ.    -   Iterating through all voxels of set Γ, verify if the voxel        center falls within any of the capsules of Π.        -   If so, count the voxel as sampled by adding it to a set Ω.    -   Calculate P as the ratio of the number of elements of the Ω and        Γ sets.

Then, the P can be calculated using the following algorithm:

$\begin{matrix}{P_{n}^{R} = \frac{N(\Omega)}{N(\Gamma)}} & \left( {{Eq}.\mspace{14mu} 7} \right)\end{matrix}$

The algorithm above calculates a scalar P(Π) value for any given biopsyplan Π of n cores and tumor of radius R.

The implementation included geometric evaluations that can be performedby classic methods available in public domain graphic toolkits. A fastway to check if a point is within the capsule FIG. 4, is to firstcalculate its distance d1 to the core axis. If d1>R, the point isexcluded. If d1<=R, then the point is included if and only if one of thefollowing relations holds: d2≤L/2 or d3≤R or d4≤R. Here, d2 is theprojected distance from the point to the core center along the axis ofthe core, and d3, d4 are distances to the ends of the core, as shown inFIG. 4.

Core positions and entry points are subject to the following anatomicalconstraints:

1. Core positions should avoid the urethra (shown in FIGS. 5A-5C) toprevent hematuria and urinary retention.

2. The needle path must not interfere with the pubic arch bone.

3. The entry point constraints depend on the biopsy path. Their presencealso reduces the rank of the state matrix defined by Eq. 6. Therefore,depending on the biopsy path, the parameterization of the plan may besimplified to a state matrix of independent variables Ψ. For the 3biopsy plans:

For transrectal biopsy the needle is normally passed alongside the TRUSprobe, which in turn is constrained at the anal sphincter, the pivotpoint of the probe. Thus, the entry points are constrained to movearound the probe circumference (circle around the ultrasound probe inFIG. 5A). Accordingly, the entry points E_(ij) are constrained to theprobe circumference and determined by the probe rotation angle θ_(i).Therefore, the state matrix Ψ (n×4) may be described as

$\begin{matrix}{\psi = \begin{bmatrix}\theta_{1} & c_{11} & c_{12} & c_{13} \\\vdots & \vdots & \vdots & \vdots \\\theta_{n} & c_{n\; 1} & c_{n\; 1} & c_{n\; 3}\end{bmatrix}} & \left( {{Eq}.\mspace{14mu} 8} \right)\end{matrix}$

For template (grid) transperineal biopsy the direction of the needlesare perpendicular to the template (parallel to each other). The entrypoints are constrained to the grid holes (FIG. 5B), discrete locationsof the template X_(ij)(x_(i1), x_(i2)). The core positions arerestricted along the direction of the needle at depth d_(i).Accordingly, the parameterized state matrix Ψ (n×3) may be described as:

$\begin{matrix}{\Psi = \begin{bmatrix}x_{11} & x_{12} & d_{1} \\\vdots & \vdots & \vdots \\x_{n\; 1} & x_{n\; 1} & d_{n}\end{bmatrix}} & \left( {{Eq}.\mspace{14mu} 9} \right)\end{matrix}$

For angled transperineal biopsy, the entry points are constrained to theperineum (FIG. 5C) and may be parameterized to points X_(ij)(x_(i1),x_(i2)) on a plane aligned with the perineum. Unlike the previous case,core center positions may be placed throughout the prostate.Accordingly, the state matrix Ψ (n×5) may be described as:

$\begin{matrix}{\Psi = \begin{bmatrix}x_{11} & x_{12} & c_{11} & c_{12} & c_{13} \\\vdots & \vdots & \vdots & \vdots & \vdots \\x_{n\; 1} & x_{x\; 2} & c_{n\; 1} & c_{n\; 1} & c_{n\; 3}\end{bmatrix}} & \left( {{Eq}.\mspace{14mu} 10} \right)\end{matrix}$

In general, the state matrix Ψ is an (n×m) matrix, with m={4, 3, 5} forthe transrectal, transperineal grid, and angled biopsies respectively.

The anatomical constraints were manually segmented from the pelvicanatomy of the Visible Human Project model to visualize the describedconstraints. In actual cases, these may be acquired from computertomography (CT) or MRI of the pelvic region if required. In case of 3DTRUS imaging, the location of the sphincter could be approximated basedon probe to image calibration. The required 3D geometric data of theprostate surface is also readily available when using novel biopsydevices such as position tracked probes and robots (Logiq-E9, GEHealthcare, Waukesha, Wis.). However, basic freehand 2D TRUS probeswould not provide the data required by the method.

The optimization problem is to find the biopsy plan Ψ that maximizes theprobability of detection of significant tumors.Maximize (^(s) P(Ψ))  (Eq. 11)

Intuitively, the algorithm should search for a solution Ψ that satisfiesthe constraints, fills the prostate as much as possible with capsules,avoids those extending out of the prostate, and minimizes theiroverlaps. The maximization may be implemented with iterative methodssuch as a gradient descent or pattern search optimization method.

Pattern search is a heuristic optimization algorithm that does notrequire the evaluation of the gradients of the objective function andwas shown to work well on functions that are not continuous ordifferentiable. Compared to the classic gradient descent method thatslides along the gradient to iteratively improve the solution, thepattern search uses a series of exploratory moves, one side and theother of each state variable, and retains the one that returns the bestgain in the objective function.

The optimization starts with an initial biopsy plan Ψ. The statevariables that determine the location of the entry points may be setzero. State variables that determine core locations may follow a sextantplan in the para-coronal plane for transrectal biopsy and transverseplane for transperineal biopsy (FIGS. 6A-6C).

At each step k, an exploratory move Δ^(k) is applied to each elementψ_(ij) ^(k−1) of the current state Ψ^(k−1), whereΔ^(k)=[δ₁, δ₂, . . . δ_(m)], where δ_(j)>0 for j=1 . . . m  (Eq. 12)

One by one, an exploratory move δ_(j) is applied to each side of eachstate matrix element while maintaining the other elements:

$\begin{matrix}{\psi_{{ij} \pm}^{expl} = \left\{ \begin{matrix}{{\psi_{qr}^{k - 1} \pm \delta_{j}},} & {q = {{i{\mspace{11mu}\;}{and}\mspace{14mu} r} = j}} \\\psi_{qr}^{k - 1} & {otherwise}\end{matrix} \right.} & \left( {{Eq}.\mspace{14mu} 13} \right)\end{matrix}$

The probability of detection ^(s)P(ψ_(ij±) ^(expl)) calculated for all 2nm exploratory moves. If any of these provides a positive gain relativeto the previous state, the move Ψ^(expl) that provided the maximum gainis retained to update the state matrix of the next iteration:

$\begin{matrix}{\psi^{k} = \left\{ \begin{matrix}{\psi^{expl}❘{{{{{Max}\left( {}^{s}{P\left( \psi_{{ij} \pm}^{expl} \right)} \right)}\mspace{14mu}{{if}\mspace{14mu}}^{s}{P\left( \psi_{{ij} \pm}^{expl} \right)}} -^{\; s}{P\left( \psi^{k - 1} \right)}} > 0}} \\{\psi^{k - 1}\mspace{14mu}{otherwise}}\end{matrix} \right.} & \left( {{Eq}.\mspace{14mu} 14} \right)\end{matrix}$

If there is no positive gain, the exploratory move Δ is reduced to:Δ^(k)=λΔ^(k−1) with parameter 0<λ<1  (Eq. 15)

When this reaches a small value, it is then reset to the initial valueΔ⁰ and the above steps are repeated to check convergence to a betteroptimal solution, until there is no improvement.

In the present case, an initial exploratory move was

$\Delta^{0} = \left\{ {\begin{matrix}{{5.0\mspace{14mu}{mm}},} & \left( {c_{ij},x_{ij},d_{i}} \right) \\10 & \left( \theta_{i} \right)\end{matrix},} \right.$the reduction parameter was λ=0.5, and the exploratory move wasconsidered small if the linear moves (c_(ij), x_(ij), d_(i)) weresmaller than 0.1 mm (6 reductions).

To simulate TRUS-biopsy and evaluate P, the male human anatomy wasreconstructed from the Visible Human Project (VHP, National Library ofMedicine). Manual segmentations of the prostate, bladder, urethra,rectum, and pubic bone with the perineal wall were done by anexperienced urologist using the Amira Visualization platform (FEICompany, Burlington, Mass.) as in FIGS. 7A and 7B. The size of theprostate, 21.4 cm³, was also measured using the Amira Visualizationplatform. To simulate different prostate volumes, the VHP's prostate wasuniformly scaled about the center of its bounding box to 5 sizes: 20cm³, 40 cm³, 60 cm³, 80 cm³, and 100 cm³.

First, to determine convergence of the optimization method, the 12-coretransrectal biopsy optimization using the typical 18 mm core length wasperformed for the 20 cm³ prostate. Optimization was started from 10different initial states (Ψ⁰). All these initial states were chosen asreasonable variants of the typical 12-core extended sextant biopsy plan(FIG. 1C), with variation in the position and orientation of the biopsyplane.

Then, the relationship between the number of cores and the size of theprostate was investigated, while maintaining the standard 18 mm corelength. For this, the ^(s)P were evaluated for 18 biopsy plans of 6 to40 cores (with increment of 2, added symmetrically on the left and rightlobes) for each of the 5 prostate sizes (20 cm³ to 100 cm³, 20 cm³increment).

Next, the relationship between the core lengths and the size of theprostate was investigated for the 12-core biopsy. For this, the ^(s)Pwere evaluated for 14 core lengths between 14 mm and 40 mm (2 mmincrement) for each of the 5 prostate sizes.

In all cases, the optimal biopsy plan Ψ was determined by maximizing thesignificant tumor probability of detection Max (^(s)P(Ψ)) for all threebiopsy paths (FIGS. 8A-8C). The probability of inadvertently detectinginsignificant tumors with the optimal plan ^(i)P(Ψ) was then evaluated,as well as the ratios of the ^(s)P to ^(i)P.

An example of a transrectal biopsy plan optimization that starts fromthe systematic biopsy plan is presented in FIG. 9 (for 12-cores, 18 mmcore length, and 40 cm³ prostate size). The initial ^(s)P of thesystematic biopsy plan was 42.5%. After optimization, the ^(s)Pincreased to 54.4%.

FIG. 10A shows the optimization result for 10 trials on a 20 cm³prostate, each manually initialized with a slightly different systematicbiopsy plane. The dotted lines denote the ^(s)P of 10 different trials,and the red solid line denotes the average of all trials. The optimizedplan has a higher ^(s)P than the systematic biopsy plan. For a 20 cm³prostate, the average ^(s)P of the initial systematic and the optimizedbiopsy plan are 61.1% and 81.8% respectively, with standard deviation of3.6% and 0.7% respectively. The average computation time of eachiteration and total computation was 0.29s(s) and 34.7(s) respectivelyusing an Intel Core 17 CPU.

The results correlating the dependency of the ^(s)P, ^(i)P, and theirratio to the size of the prostate for a constant 18 mm biopsy corelength are represented in FIGS. 11A-11C. These FIGS. show that if morecores are sampled the P increases, and the number of cores required toachieve a certain ^(s)P level is higher for larger prostates. The ^(s)Pand ^(i)P are similar for different biopsy paths, with slightly higher^(s)P values for the transrectal, then the angled transperineal, thenthe template transperineal biopsy (FIG. 11A).

At the same time, when more cores were used the ^(i)P also increased asin FIG. 11B. The ^(s)P to ^(i)P ratio decreased with the number of coresfor all 3 biopsy paths as in FIG. 11C. For a 12-core extended sextanttransrectal biopsy (18 mm) on a 40 cm³ prostate, the ^(s)P and ^(i)Pwere 54.1% and 28.0% respectively, and the ^(s)P to ^(i)P ratio was 1.9.

For prostate sizes larger than 60 cm³, 99% ^(s)P couldn't be reachedeven with 40 cores. Before the ^(s)P curves reached the saturationpoint, these were approximately linear, so that the number of coresrequired to achieve the same ^(s)P level is proportional to the prostatevolume.

FIGS. 12A-12C depicts the dependency of the probability of cancerdetection on the length of the biopsy cores for the common 12-coreextended biopsy. The ^(s)P increases with the length of the core, asillustrated in FIG. 12A. This saturates at a length that is close to thedepth of the prostate in the direction of biopsy (90% @ 25 mm for a 20cm³ prostate). The increase in the core length is also followed byincreased ^(i)P (FIG. 12B). Before saturation, ^(s)P and ^(i)P wereapproximately linear to the core length. The ratio of ^(s)P to ^(i)Pdecreased with the core length for all 3 biopsy paths (FIG. 12C).

A Capsule Model is presented to facilitate the evaluation of theprobability of prostate cancer detection that a biopsy plan may yield.This model may be subsequently used to optimize the biopsy plan geometryby maximizing the likelihood of cancer detection with a given number ofbiopsy cores.

Traditional systematic biopsy methods use a uniform distribution ofcores throughout the prostate gland. However, these lack a cleargeometric definition leaving room for subjective interpretation. Thebiopsy plans presented herein are fully defined by coordinates of thecores and their direction. Together with the Capsule model, these plansenabled the quantification of cancer detection likelihood andoptimization of the biopsy plan. For example, the probability ofsignificant cancer detection with 12 cores in a 20 cm³ prostate is 61.1%for the sextant plan and may be optimized to 81.8%, assuming that bothof these plans are perfectly executed. In real practice, withconventional freehand TRUS biopsy, the probability of significant cancerdetection of the sextant was found to average only 43%, due to manualexecution errors and subjective planning. Together, these resultssuggest that the biopsy may be improved by almost 40% by using optimizedplanning and precise biopsy methods such as robot-assisted biopsytargeting.

Moreover, the numerical results reported herein represent worst-casescenarios, where the tumors would all be at the clinically significantsize limit (0.5 cm³). Since actual tumors would frequently be larger,the values that were reported are the lowest detection rates to beexpected. For the example above, a wel executed optimal plan would yieldat least 81.8% detection, but may be as high as 100% if tumors arelarger. This is further supported by the spherical shaped tumor modelthat is also the worst case scenario in this respect. The resultspresented herein are intuitive and agree with previously reportedresults, which showed that more and longer biopsy cores are needed forlarger prostates up to a saturation limit. The findings are also inagreement with a recent study, which showed that increasing the corelength and number in the anterior regions of the prostate improved thedetection rate for clinically significant cancer.

Several groups have also reported quantitative cancer detection ratesand proposed optimization methods. A recent study reported that thesextant 12-core biopsy plan with 2-4 additional anteriorly directedcores, all taken with a 22 mm core length, may yield 100% detection rateof the significant tumors in prostates≤50 cm³. The results are inagreement since their tumor sizes ranged from 0.5 cm³ to 5.0 cm³, asdiscussed above.

With the shared experience of the prior studies, the model could befurther updated to predict not only the lowest but also the expecteddetection rate, by using whole mounted prostate models in addition tothe Visible Human Project model currently used.

On the other hand, other studies reported that 100% detection may not beachievable even with numerous cores, in other words that even thesaturation biopsy may not saturate. Unfortunately, the results alsoagree with this finding. For example, if a 60 cm³ prostate would haveonly one 0.5 cm³ tumor, there would be at least 10% chance of missing iteven with a perfectly executed biopsy of 40 cores (FIG. 11a ).

The capsule model also enables the estimation of the risk of overdiagnosing prostate cancer at biopsy, that is the risk of detectinginsignificant cancer (<0.2 cm³). The present invention provides for theprobability of detecting insignificant cancer.

Results shows that the risk of detecting insignificant cancer (^(i)P) isa tradeoff of sampling more biopsy cores with the purpose of detectingsignificant cancer (^(s)P). Moreover, ^(i)P increases faster than ^(s)Pwith the number of cores, and especially for many cores and/or smallerprostates. Thus, careful consideration for overdetection should be givenwhen increasing the number of cores, according to graphs presented(FIGS. 11A-11C).

Herein the methods are applied to a Visible Human Project model. Themethods could be applied to biopsy optimization in individual patients,provided that 3D imaging is available. A proper balance of theinsignificant/significant probability of detection could be made inconcordance with the number of cores required for the patient. Theultimate goal would be to determine the biopsy plan that would detectall significant tumors utilizing the lowest number of biopsy cores, andthus minimizing the probability of insignificant tumor detection as wellas invasiveness. Moreover, even if the biopsy result is negative forprostate cancer, the biopsy plan would numerically give the likelihoodof a false-negative result occurring, and thus help the management ofdisease.

In this example the analysis and results focused on decoupling theeffect of the number of cores and the core length on the probability ofcancer detection. However, performing the study exhaustively for all 3biopsy paths, 5 prostate sizes, 18 core number sets, and 14 core lengthsis feasible and has actually been performed. However, displaying thesemassive data in a comprehensive manner was challenging. Therefore, forthe purpose of this application only selected data that is relevant tothe methods and from a clinical standpoint is presented.

In addition to traditional sextant methods, several studies have used 3Dbiopsy planning and considered the direction of the cores not only theircore center position. In this example, the directionality of the coreplanning was improved by using realistic anatomical locations for needleaccess. Consideration of the limited access to the prostate caused bythe constraints of the human anatomy makes the plans more realistic andpractically applicable, including the depth of the cores.

Integrating the site of needle access with planning, as presented, setsimaging requirements that are both limiting and enabling. Imagingcapable of reconstructing the prostate in 3D are required, such astracked TRUS, CT, or MRI. In this respect, the methods presented applydirectly to modern biopsy devices such as mechanically and magneticallytracked (Logiq-E9, GE Healthcare, Waukesha, Wis.) TRUS probes, imagefusion systems (KOELIS, La Tronche, FRANCE) TRUS robots, as well asMRI-Safe robots. In turn, the use of these novel biopsy devices wouldsubstantially improve upon the accuracy of executing the proposedoptimized biopsy plans.

The analytical model is based on several idealized assumptions. First,tumors are considered to be spherical shape rather than irregular,curvilinear, or fusiform. While this does not reduce the validity of theoptimization, it does limit the use of the proposed methods inpredicting the size of detected tumors. However, the size may bepredicted by other methods that consider the length of the cancerouspart of the biopsy core.

Second, the model assumes that tumors are evenly distributed within thegland while it is reported that approximately 68% originate from theperipheral zone (PZ) and 32% from the central gland (CG). Thisassumption may explain that ^(s)P are similar for the transrectal, andtransperineal biopsy paths in the present invention, and that therequired number of cores is directly correlated to the prostate size.

Both limitations may be overcome with further research, by correlatingstatistical information of tumor shape and zonal distribution from wholemount prostates. This additional information would further improve thealgorithm to apply higher weight factors in high risk zones andaccordingly distribute more cores in these regions.

The Capsule Model allows 3D geometric optimization of biopsy corepositions and orientations based on 3D prostate imaging. As with allsystematic biopsy methods, evenly distributing the cores increases theprobability of cancer detection by preventing the cores being clusteredor missing regions. While traditional sextant biopsy plans lack thegeometric blueprint of the plan, the proposed plans are defined bycoordinates, optimized in a geometric sense, and consider anatomicconstraints of the biopsy path, either transrectal or transperinealapproach. Results showed that more and longer cores are required forhigher probability of detection and in larger glands. However, thesealso increase the biopsy-associated morbidities and detection ofinsignificant cancer which may contribute to PCa overdetection. Theresults may be used to balance the number of biopsy cores based onsignificant/insignificant detection expectancy, in addition to otherclinical considerations. The present invention is the first toquantitatively estimate the insignificant portion.

It should be noted that the computer application is programmed onto anon-transitory computer readable medium that can be read and executed byany of the computing devices mentioned in this application. Thenon-transitory computer readable medium can take any suitable form knownto one of skill in the art. The non-transitory computer readable mediumis understood to be any article of manufacture readable by a computer.Such non-transitory computer readable media includes, but is not limitedto, magnetic media, such as floppy disk, flexible disk, hard disk,reel-to-reel tape, cartridge tape, cassette tapes or cards, opticalmedia such as CD-ROM, DVD, Blu-ray, writable compact discs,magneto-optical media in disc, tape, or card form, and paper media suchas punch cards or paper tape. Alternately, the program for executing themethod and algorithms of the present invention can reside on a remoteserver or other networked device. Any databases associated with thepresent invention can be housed on a central computing device,server(s), in cloud storage, or any other suitable means known to orconceivable by one of skill in the art. All of the informationassociated with the application is transmitted either wired orwirelessly over a network, via the internet, cellular telephone network,RFID, or any other suitable data transmission means known to orconceivable by one of skill in the art.

Although the present invention has been described in connection withpreferred embodiments thereof, it will be appreciated by those skilledin the art that additions, deletions, modifications, and substitutionsnot specifically described may be made without departing from the spiritand scope of the invention as defined in the appended claims.

The invention claimed is:
 1. A method of biopsy planning comprising:calculating significant and insignificant tumor detection probability,wherein significance is based on tumor size; generating athree-dimensional biopsy plan that increases the probability of thesignificant and insignificant tumor detection probability; calculatingprobability of a false negative detection of tumor using thethree-dimensional biopsy plan to create a revised three-dimensionalbiopsy plan; and determining a number and length of biopsy coresrequired to execute the revised three-dimensional biopsy plan.
 2. Themethod of claim 1 further comprising implementing the method using anon-transitory computer readable medium.
 3. The method of claim 1further comprising: setting a bounding box for a tumor detection areaand a voxel size to discretize this volume at a predetermined level ofresolution; iterating through all voxels; checking if a voxel center iswithin the tumor detection area, and if so add it to a set Γ; iteratingthrough all voxels of set Γ; verifying if the voxel center falls withinany of the biopsy cores of a set Π; counting the voxel with a centerthat falls within any of the biopsy cores of set Π as sampled by addingit to a set Ω; and calculating tumor prediction probability as the ratioof the number of elements of the Ω and Γ sets.
 4. The method of claim 1further comprising: setting a volume of a tumor detection area and avoxel size to discretize the volume of the tumor detection area at apredetermined level of resolution to a set of voxels Γ; defining thetumor detection area of a biopsy core as a capsule surrounding thebiopsy core with a cylindrical volume having hemispherical end caps ofthe diameter of the tumor to be detected; iterating through all voxelsof Γ and checking if a voxel center is within the tumor detection areaof the biopsy cores of the plan; adding the voxel center to the sampledvoxel set Ω; and calculating tumor prediction probability as the ratioof the number of elements of the detected voxel set Ω and tumor searcharea voxel set Γ.
 5. The method of claim 1 further comprising detectingtumors in the prostate gland.
 6. The method of claim 1 furthercomprising detecting tumors in any organ with a boundary that issegmentable as a surface.
 7. The method of claim 1 further comprisingrepresenting the biopsy cores as a capsule with a cylindrical volumehaving hemispherical end caps.
 8. The method of claim 1 furthercomprising setting a tumor detection area.
 9. The method of claim 1further comprising generating the three-dimensional biopsy plan forsignificant tumors for a predefined number of biopsy cores and lengths.10. The method of claim 1 further comprising generating thethree-dimensional biopsy plan for insignificant tumors for a predefinednumber of biopsy cores and lengths.
 11. The method of claim 1 furthercomprising defining a tumor detection area of a biopsy core as a capsulesurrounding the biopsy core with a cylindrical volume havinghemispherical end caps of the diameter of a tumor to be detected.
 12. Asystem for biopsy planning comprising: a source of image data capable ofreconstructing a target organ in three-dimensions; a non-transitorycomputer readable medium programmed for: calculating significant andinsignificant tumor detection probability from the image data, whereinsignificance is based on tumor size; generating a three-dimensionalbiopsy plan that increases the probability of the significant andinsignificant tumor detection probability; calculating probability of afalse negative detection of tumor using the three-dimensional biopsyplan to create a revised three-dimensional biopsy plan; and determininga number and length of biopsy cores required to execute the revisedthree-dimensional biopsy plan.
 13. The system of claim 12 furthercomprising a computing device.
 14. The system of claim 12 furthercomprising: setting a bounding box for a tumor detection area and avoxel size to discretize this volume at a predetermined level ofresolution; iterating through all voxels; checking if a voxel center iswithin the tumor detection area, and if so add it to a set Γ; iteratingthrough all voxels of set Γ; verifying if the voxel center falls withinany of the biopsy cores of a set Π; counting the voxel with a centerthat falls within any of the biopsy cores of set Π as sampled by addingit to a set Ω; and calculating tumor prediction probability as the ratioof the number of elements of the Ω and Γ sets.
 15. The system of claim12 further comprising: setting a volume of a tumor detection area and avoxel size to discretize the volume of the tumor detection area at apredetermined level of resolution to a set of voxels Γ; defining thetumor detection area of a biopsy core as a capsule surrounding thebiopsy core with a cylindrical volume having hemispherical end caps ofthe diameter of the tumor to be detected; iterating through all voxelsof Γ and checking if a voxel center is within the tumor detection areaof the biopsy cores of the plan; adding the voxel center to the sampledvoxel set Ω; and calculating tumor prediction probability as the ratioof the number of elements of the detected voxel set Ω and tumor searcharea voxel set Γ.
 16. The system of claim 12 further comprisingdetecting tumors in the prostate gland.
 17. The system of claim 12further comprising detecting tumors in any organ with a boundary that issegmentable as a surface.
 18. The system of claim 12 further comprisingrepresenting the biopsy cores as a capsule with a cylindrical volumehaving hemispherical end caps.
 19. The system of claim 12 furthercomprising setting a tumor detection area.
 20. The system of claim 12further comprising a biopsy device.